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Four numbers are chosen at random (witho...

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}. Statement-1: The probability that the chosen numbers when arranged in some order will form an AP Is `1/(85)` . Statement-2: If the four chosen numbers from an AP, then the set of all possible values of common difference is {1, 2, 3, 4, 5}.

Text Solution

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`a= 1 ; d= 1; {1,2,3,4,17,18,19,20,17}`
`d= 2 ; {1,3,5,7, 14,16,18,20,14}`
`d=3 ; {1,4,7,10,11,14,17,20}`
P(4 are in AP) = `(17+2)/2 xx6/(.^20C_4) = 57/(.^20C_4)`
`= (57 xx 4 xx 3 xx 2)/(20 xx 19 xx 18 xx 17) = 1/85`
option 2 is correct
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